OOC:en:3.4 The Processor

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How do we process an expression? If we only want to perform simple arithmetic on numerical values, we can extend the recognition functions and compute the result as soon as we recognize the operators and the operands: sum() would expect a double result from each call to product(), perform addition or subtraction as soon as possible, and return the result, again as a double function value.

If we want to build a system that can handle more complicated expressions we need to store expressions for later processing. In this case, we can not only perform arithmetic, but we can permit decisions and conditionally evaluate only part of an expression, and we can use stored expressions as user functions within other expressions. All we need is a reasonably general way to represent an expression. The conventional technique is to use a binary tree and store token in each node:

   struct Node { 
       enum tokens token; 
       struct Node * left, * right; 
   };

This is not very flexible, however. We need to introduce a union to create a node in which we can store a numerical value and we waste space in nodes representing unary operators. Additionally, process() and delete() will contain switch statements which grow with every new token which we invent.